Drinking coffee in a non-kosher place

A business that is open on Shabbat is not prohibited from using its services. However, if because it is open there is no supervision, one should be wary of kosher issues. Regarding coffee or beer, there should not be a problem, even if the dishes are not immersed, there is room for leniency in this. I assume that these are not dishes used for meat and milk, etc. Regarding a cup of coffee, it is worth checking whether it was washed together with meat dishes.